8 grade maths

The polynomial 8 is of degree?
(a) 1
(b) 1/2
(c) 8
(d) 0

Aniket Singh

11 Months agoGrade

2 Answers

Askiitians Tutor Team

Approved Tutor Answer11 Months ago

To determine the degree of the polynomial 8, we need to understand what the degree of a polynomial actually represents. The degree of a polynomial is defined as the highest power of the variable in the expression. However, in this case, the polynomial is simply the constant number 8, which can be thought of as 8x^0, since any number raised to the power of zero is 1.

Understanding Polynomial Degrees

Polynomials are mathematical expressions that can include constants, variables, and exponents. The general form of a polynomial can be expressed as:

a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀

In this expression, the degree is determined by the term with the highest exponent (n). For example, in the polynomial 3x⁴ + 2x² + 5, the degree is 4 because that is the highest exponent present.

Analyzing the Given Polynomial

Now, let’s apply this understanding to the polynomial in question, which is simply the constant 8. Since it does not contain any variables, we can express it as:

8 = 8x⁰

Here, the exponent of x is 0, which means that the degree of the polynomial is 0. This is a key point because it shows that even though the polynomial is a constant, it still has a degree associated with it.

Final Thoughts on Polynomial Degrees

In summary, the degree of the polynomial 8 is 0. Therefore, the correct answer to your question is (d) 0. Understanding the degree of polynomials is crucial in various mathematical contexts, including calculus and algebra, as it helps in analyzing the behavior of functions and their graphs.

Askiitians Tutor Team

Approved Tutor Answer11 Months ago

To determine the degree of the polynomial 8, we first need to understand what a polynomial is and how its degree is defined. A polynomial is an expression that can include constants, variables, and exponents, and it is typically written in the form of a sum of terms. The degree of a polynomial is the highest power of the variable in the expression. However, in this case, we have a constant polynomial.

Identifying the Degree of a Constant Polynomial

The polynomial given is simply the number 8. This can be viewed as a polynomial with no variable present. In mathematical terms, we can express it as:

8 = 8x^0

Here, we see that the term 8 can be rewritten with the variable x raised to the power of 0. This is because any non-zero number raised to the power of 0 equals 1. Thus, the expression simplifies to 8, confirming that it is indeed a constant polynomial.

Understanding the Degree

In the context of polynomials, the degree is defined as follows:

For a polynomial with one or more terms, the degree is the highest exponent of the variable.
For a constant polynomial (like 8), which does not contain any variable, the degree is defined to be 0.

Therefore, since 8 does not have any variable component, we conclude that its degree is 0. This leads us to the correct answer among the options provided.

Final Answer

The degree of the polynomial 8 is (d) 0. This is a fundamental concept in algebra, and recognizing the degree of polynomials, including constant ones, is crucial for understanding more complex polynomial functions in mathematics.